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International Journal of Mathematics and Mathematical Sciences
Volume 29, Issue 5, Pages 279-283
http://dx.doi.org/10.1155/S0161171202007147

On the continuity of principal eigenvalues for boundary value problems with indefinite weight function with respect to radius of balls in N

Department of Mathematics, Faculty of Basic Sciences, Mazandaran University, Babolsar, Iran

Received 19 March 2001

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We investigate the continuity of principal eigenvalues (i.e., eigenvalues corresponding to positive eigenfunctions) for the boundary value problem Δu(x)=λg(x)u(x), xBR(0);u(x)=0, |x|=R, where BR(0) is a ball in N, and g is a smooth function, and we show that λ1+(R) and λ1(R) are continuous functions of R.